A092634 a(n) = 1 - Sum_{k=2..n} k*k!.

-3, -21, -117, -717, -5037, -40317, -362877, -3628797, -39916797, -479001597, -6227020797, -87178291197, -1307674367997, -20922789887997, -355687428095997, -6402373705727997, -121645100408831997, -2432902008176639997

Offset

2,1

References

Appeared in University of Texas Interscholastic League High School Number Sense District Test, 2004.

Links

G. C. Greubel, Table of n, a(n) for n = 2..445

Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

Formula

Conjecture: a(n) +(-n-3)*a(n-1) +(2*n+1)*a(n-2) +(-n+1)*a(n-3)=0. - R. J. Mathar, Sep 27 2014

a(n) = 3 - (n+1)!. - Michel Marcus, Jun 07 2020

From G. C. Greubel, Jun 07 2020: (Start)

a(n) = 3 - !(n+2) + !(n+1) = 3 - A003422(n+2) + A003422(n+1).

E.g.f.: 3*exp(x) - (3 - 3*x + x^3)/(1-x)^2. (End)

Maple

A092634:= n-> 3-(n+1)!: seq(A092634(n), n=2..20); # G. C. Greubel, Jun 07 2020

Mathematica

Table[i; 1 - Sum[n n!, {n, 2, i}], {i, 2, 20}]

Prog

(PARI) a(n) = 1 - sum(k=2, n, k*k!); \\ Michel Marcus, Jun 07 2020
(Sage) [3-factorial(n+1) for n in (2..20)] # G. C. Greubel, Jun 07 2020

Crossrefs

Cf. A033312.

Sequence in context: A309670 A121140 A005057 * A178537 A046727 A084159

Adjacent sequences: A092631 A092632 A092633 * A092635 A092636 A092637

Keyword

sign

Author

Doug Ray (draymath(AT)iastate.edu), Apr 11 2004

Status

approved